It is well-known that an important task of the artificial intelligence is to make computer simulate human being in dealing with certainty and uncertainty in information. Logic gives a technique for laying the foundations of this task. Information processing dealing with certain information is based on the classical logic. Non-classical logic includes many valued logic and fuzzy logic which takes the advantage of the classical logic to handle information with various facets of uncertainty (Zadeh in Inform Sci, 172:1–40, 2005, ), such as fuzziness and randomness. Therefore, non-classical logic has become a formal and useful tool for computer science to deal with fuzzy information and uncertain information.